79 



whore '^ is ttie ratio of the specific heats, we may set 



° - /^ ^^ = ^' w^ (i'f^' '1°' 



If v;e set x b a'^, the kinetic energy term of (1) Is 



If we expand the potential energy terms in powers of 

 (x - X ), where x, s a, , v;e find 



Potential energy = constant -f- |~ Tf/Poo x, (x-x^)-f ••• (12) 



From (11) and (12) the limiting period for smoll oscillations 

 coraes out as 



Ko detailed calculation of the period for inter- 

 mediate cases will be attempted here. T?ie order of ir.ag- 

 nitude of the deviation from (0) caused by gas pressure 

 can, hov/ever, be eotinated as follows, nince in (13) the 

 radius a, is the nean of the raaxlraum and minimum radii for 

 the small oscillations, it is tempting to rev^rite (0) in 



tarns of the Koan of the two radii a and 0. If this is 



max 



done by putting 



1 4 ■^ 



^me&n = ^ ^ max » 3 T^ ^niax P 00 = W , 



and if in (13) we take "jT's 1.4 to get a numerical value, we 

 find from (0) and (13) respectively 



